A, B and C can do a certain job working alone in 50 days, 75 days and 20 days respectively. They all work together on the job for 4 days, after which C leaves. For the remaining work, only A and B continue. How many additional days will A and B together take to finish the rest of the job?

Introduction / Context:
This time and work question deals with three workers who initially work together, and then one of them leaves. It tests the ability to calculate combined work done in a certain number of days and to then compute the remaining work for the remaining workers. Such staged work problems frequently appear in aptitude examinations.

Given Data / Assumptions:
- A alone can complete the job in 50 days.
- B alone can complete the job in 75 days.
- C alone can complete the job in 20 days.
- A, B and C work together for 4 days, then C quits and only A and B continue.
- We assume the total work is 1 complete job and that each worker's speed is constant.

Concept / Approach:
We first convert each individual time into a daily work rate. Then we find the combined rate of A, B and C together and compute how much of the job is completed in the first 4 days. The remaining work is then completed only by A and B working together, so we use their combined rate to determine the extra days required to finish the job.

Step-by-Step Solution:
Step 1: Let total work = 1 unit. Step 2: A's rate = 1/50 per day, B's rate = 1/75 per day, C's rate = 1/20 per day. Step 3: Combined rate of A, B and C = 1/50 + 1/75 + 1/20. Step 4: Compute combined rate. Using common denominator 300: 1/50 = 6/300, 1/75 = 4/300, 1/20 = 15/300, so total = 25/300 = 1/12 per day. Step 5: Work done in 4 days by all three = 4 * (1/12) = 4/12 = 1/3 of the job. Step 6: Remaining work = 1 − 1/3 = 2/3 of the job. Step 7: After C leaves, only A and B work, so combined rate of A and B = 1/50 + 1/75. Step 8: With denominator 150, 1/50 = 3/150 and 1/75 = 2/150, so A and B together do 5/150 = 1/30 per day. Step 9: Time required for A and B to finish remaining 2/3 of the job = (2/3) / (1/30) = (2/3) * 30 = 20 days.

Verification / Alternative check:
Confirm the logic by reconstructing work done. In the first 4 days, they complete 1/3. In the next 20 days, A and B together work at 1/30 per day, so work done = 20 * 1/30 = 2/3. Total work = 1/3 + 2/3 = 1 job. The numbers fit perfectly, confirming that 20 days is correct for the second phase of the work.

Why Other Options Are Wrong:
Option 30 days: This would result in more than 1 full job when combined with the first 4 days of work.
Option 18 days: This gives less than 2/3 of the job for A and B in the second phase and the total work would be incomplete.
Option 24 days: Leads to more work than required since 24 * 1/30 = 4/5, and 1/3 + 4/5 is greater than 1.

Common Pitfalls:
Students sometimes forget to compute the exact fraction of work remaining after the first phase or mix up individual and combined rates. Another common mistake is to subtract days instead of converting to rates. Always calculate how much work is done in each phase based on daily rates, then find the remaining work and the time taken to finish it.

Final Answer:
A and B together will take an additional 20 days to complete the remaining work.